How I teach cumulative voting

It wasn’t always this way. I remember quite well the first couple of semesters that I taught Business Associations. My attempts to teach cumulative voting were — err, not particularly successful.

I would explain that, by default in a Model Act jurisdiction, corporations have straight voting. For every director, it’s a fresh vote. Majority always wins, every time. (Plurality wins, really, but majority ownership always satisfies that threshold.) This approach leaves many minority shareholders unhappy.

And then we’d go over the formula. For cumulative voting, we determine each shareholder’s number of votes by multiplying the number of directors up for election by that shareholder’s number of shares. Each shareholder can then apportion her votes however she wants to. This, in theory, allows minority shareholders to guarantee (as long as they are above a certain threshold) some level of board representation.

And as I talked, eyes would glaze over. Students would take on the deer-in-headlights look. I’d ask for questions. No one would say a thing. I’d try to go through some example on the chalkboard. Okay, suppose that Shareholder A has X many votes, and Shareholder B has Y many votes. The chalkboard would be covered in numbers. More eyes would glaze over. I would reference the formula set out in the book. ((Shares voting / (directors + 1)) + 1 = shares required).

By the end of the day, I would have spent far too much time trying to make the topic comprehensible — and I’d still suspect that less than half the class really understood it. (And come test time, that suspicion was borne out.) It was one of my least favorite topics to teach.

And then I hit on the idea of M&Ms. It’s no exaggeration to say that this has pretty much solved the problem.

The initial student fear is still there. As we move into cumulative voting, students look up apprehensively. They’ve read the book on it, and they’ve had a hard time understanding. The math frightens them.

They have nothing to worry about. They will understand perfectly by the end of class. And it will be fun.

I ask for two student volunteers. They need to be relatively good natured, unafraid of math, smart enough to think through some basic problems. They will be my shareholders. They come to the front of the room.

I explain that A owns 6 shares of the company and B owns 4 shares. A wants to elect people from the right side of the room onto the board. B wants to elect people from the left side. There are five directors up for election.

We quickly go over straight voting. Who wins the vote for Director 1? A. For director 2? A. And so on. A wins them all. It’s easy to see. And I point out, B owns 40% of the company, but doesn’t elect a single person onto the board. Is that really fair?

And then I bring out a bag of M&Ms. And we count cumulative votes.

5 directors. 6 shares. A receives 30 M&Ms. And B receives 20 M&Ms. They will be able to allocate these M&Ms any way that they want to. They can allocate any number of their M&Ms to any students from their respective side of the class. The top five vote-getters are in.

The two shareholders start to calculate what they’re going to do with their M&Ms. Around the class, eyes light up. These aren’t abstract numbers on the board anymore. These are concrete, and very easy to see. (And the milk chocolate melts in your mouth, not in your hand!) The idea starts to make sense. People begin to call up suggestions to the volunteers.

It becomes very evident very quickly to the shareholders, that if B allocates 10 of her M&Ms each to two candidates, there is simply no way that A can block those candidates. Sure, A could allocate 11 M&Ms to a few other candidates. But then A runs out of M&Ms to use — she has only 8 M&Ms left. As long as B is smart with her voting, there is simply no way that A will be able to keep B’s top two candidates off of the Board. And similarly, A can lock up at least three seats herself.

Of course, either shareholder can blow it with foolish allocations. Either one could stack all of her M&Ms on one candidate, giving the other four seats away without a fight. But as long as both of them act rationally, the Board will end up with 2 of B’s candidates, and 3 of A’s. The students can see it happen, right in front of them, in bright colors. It makes sense.

After the exercise, the students eat their votes, and I pass around the bag of leftover cumulative votes for the class to munch on.

For the rest of the semester, every time we mention cumulative voting, I will refer to it as stacking one’s M&Ms on a particular candidate. Students will grin. It’s not a concept they’re afraid of anymore. And the lesson seems to stick — I tested the concept as a short answer a few semesters ago, and almost the entire class nailed it.

There will still be difficult topics to teach. But cumulative voting is no longer one of them.

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What particularly effective tricks or example do you use for teaching those especially frustrating topics?

3 Responses

I use slides for cum voting, on the course web site long before and after the lesson. It is better than writing on the board each time, but maybe not as a good as M&Ms.

A nice thing about the slides is to illustrate how effects change with board size and boards with staggered terms. The slides are duplicated sequentially using strike-through for numbers from previous examples to show changes readily.

The dilutive effects of share issuances, and preemptive rights to protect holders, pose challenges akin to those you describe for cumulative voting. I don’t know if M&Ms would work for that , but I also use advance slides to illustrate and it seems to work.

Some years back, the State Department has sent some touring francophone Africans to Birmingham. I was invited to explain limited and cumulative voting to them (because of my vote-dilution cases in Alabama which were settled with LV and CV).

The State Department interpreter was not well-versed in political science or law, and so was having a hard time translating my remarks. I hit upon the idea of using coins. I pulled a bunch of quarters out of my pocket and said, “Everyone has 7 votes.” I piled the 7 quarters in several different ways. The Africans beamed. The interpreter was relieved.

That’s a very imaginative way to get the point across. But it’s also a sad reflection on the quantitative skills of your students, all of whom are college graduates whose grades were good enough to get them into law school. How are they going to be able to interpret, much less draft, contracts with antidilution provisions, complex proportional allocations, etc.?